Answer
$x=\frac{27}{64}$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{\frac{3}{4}}x=3$ is equivalent to $(\frac{3}{4})^{3}=x$.
Therefore, $x=(\frac{3}{4})^{3}=\frac{3\times3\times3}{4\times4\times4}=\frac{27}{64}$.